MELBOURNE, Australia (AP) — Angelique Kerber remains the only Grand Slam singles winner in the Australian Open women's draw after avoiding a major upset.

For a while it appeared Kerber's progression could unravel against No. 88 Hsieh Su-wei, a former top-ranked doubles player with a double-handed grip on both sides.

But former No. 1 Kerber held her composure and finally got a succession of breaks to finish off the second set and dominate the third in a 4-6, 7-5, 6-1 victory Monday afternoon that earned her a quarterfinal spot against U.S. Open finalist Madison Keys.

Defending champion Roger Federer had no such difficulties in reaching the Australian Open quarterfinals for the 14th time, accounting for Marton Fucsovics 6-4, 7-6 (3), 6-2. The 19-time major winner had never played Fucsovics but had beaten his coach—Attila Savolt—here in the second round in 2002.

Federer will renew a lengthy rivalry next against Tomas Berdych, who returned to the quarterfinals for the seventh time at Melbourne Park with a 6-1, 6-4, 6-4 win over Fabio Fognini.

Federer leads their career head-to-heads 19-6, including all four times they've met in Melbourne and in the Wimbledon semifinals last year.

The win over Fucsovics was Federer's first day match of the 2018 tournament, and he joked about needing sunglasses and a towel for the beach but said really the only change was to set the alarm for a different time.

With a mix of slice and chips, lobs and bunts, whippy half-volleys and wristy crosscourt ground strokes off both wings, Hsieh pushed Kerber to the extremes and unsettled her rhythm.

Former No. 1-ranked Kerber finally got a succession of breaks to take the second set and dominate the third in a 4-6, 7-5, 6-1 victory on Monday afternoon that gave her a 13th straight win in 2018.

''Credit to her. She played an unbelievable match,'' said Kerber, who won the Australian and U.S. Open titles and reached No. 1 in 2016. ''I was feeling I was running everywhere.

''Actually, I'm really happy about how I was able to change the match and turn around and playing, then, good tennis again in important moments, especially in the third set.''

Keys returned to the quarterfinals here for the first time in three years with a 6-3, 6-2 win over No. 8-seeded Caroline Garcia, and is yet to drop a set so far.

Top-seeded Simona Halep has had her troubles in Melbourne, including first-round exits in 2016 and '17 and having to rally from triple match point down to advance through the third round this time.

The two-time French Open finalist, who is also contending with a left ankle injury, beat Naomi Osaka 6-3, 6-2 to return to reach the quarterfinals here for the third time.

Hsieh, contesting the fourth round in a major for the first time in a decade, certainly made the most of her time back in the spotlight.

The Taiwanese player took out one major winner—Wimbledon champion Garbine Muguruza—in the second round, and took the first set of Kerber.

That forced Kerber, returning from a form slump that saw her ranking drop into the 20s in 2017, to produce some of her best tennis.

She finished a 14-shot rally early in the second set by racing to the net and reaching at full stretch to track down a drop shot and send a forehand winner over the net post.

Kerber had to serve to stay in the match in the second set. Then, after converting a break-point chance with a sliding forehand winner down the line, Kerber crouched and screamed to celebrate the point.

She served out the second set at love and then got critical service breaks in the first and fifth games of the third.

Hsieh has won two Grand Slam doubles titles, and was ranked No. 1 in doubles in 2014. At age 32, she was oldest woman still in the singles draw, and possibly the wiliest.

''I like to play freestyle,'' Hsieh said. ''Like today I go on the court, if I don't have a plan then I do whatever I can.''